In combinatorial game theory, an impartial game is a game in which the allowable moves depend only on the position and not on which of the two players...

available to the other as well. One such game is Nim, which can be solved completely. Nim is an impartial game for two players, and subject to the normal...

In combinatorial game theory, a game is partisan (sometimes partizan) if it is not impartial. That is, some moves are available to one player and not...

that every impartial game is equivalent to a nim game with a single pile. Variants of nim have been played since ancient times. The game is said to have...

combinatorial game theory, the Sprague–Grundy theorem states that every impartial game under the normal play convention is equivalent to a one-heap game of nim...

sacrifices through earlier play. In combinatorial game theory, Dots and Boxes is an impartial game and many positions can be analyzed using Sprague–Grundy...

states that every impartial game is equivalent to a Nim heap of a certain size, nimbers arise in a much larger class of impartial games. They may also...

therefore an impartial game. Dé d’Or des Créateurs de Jeux 1989 – Paris, France Oscar du Jouet – Toy Oscar 1992 – Paris, France Jouet de l'année – Game of the...

Cram is a mathematical game played on a sheet of graph paper (or any type of grid). It is the impartial version of Domineering and the only difference...

tic-tac-toe is an impartial game similar to tic-tac-toe. However, in this game players can choose to place either X or O on each move. This game can also be...

Notakto is a tic-tac-toe variant, also known as neutral or impartial tic-tac-toe. The game is a combination of the games tic-tac-toe and Nim, played across...

Taking the most card tricks In combinatorial game theory, the normal play convention of an impartial game is that the last player able to move is the winner...

without suffix characteristic able rule table ran run . Partisan game Impartial game Solved game Steinhaus, H. (1999). Mathematical Snapshots (3rd ed.). New...

Kayles is a simple impartial game in combinatorial game theory, invented by Henry Dudeney in 1908. Given a row of imagined bowling pins, players take turns...

in combinatorial game theory to assign nim-values to impartial games. According to the Sprague–Grundy theorem, the nim-value of a game position is the...

as a generalization of Nim, Kayles, and similar games. Octal games are impartial meaning that every move available to one player is also available to the...

Sprouts is an impartial paper-and-pencil game which can be analyzed for its mathematical properties. It was invented by mathematicians John Horton Conway...

result is the game Dawson's chess. The game was invented by Thomas Rayner Dawson in 1935. Dawson's chess reduces to the impartial game denoted .137 in...

of Hackenbush, any player is allowed to cut any edge: as this is an impartial game it is comparatively straightforward to give a complete analysis using...

coins. The game is usually played as a normal play game, which means that the player who removes the last coin wins. It is an impartial game, meaning that...

In combinatorial game theory, and particularly in the theory of impartial games in misère play, an indistinguishability quotient is a commutative monoid...

Sprague–Grundy theorem applies to impartial games (in which each move may be played by either player) and asserts that every such game has an equivalent Sprague–Grundy...

that one be randomly determined. For a game to be one of skill, a starting position needs to be chosen by impartial means. Some games, such as Arimaa and...

In combinatorial game theory, for an impartial game given in explicit form as a directed acyclic graph whose vertices represent game positions and whose...

available to them, the game is impartial; otherwise the game is partisan. The set of colors could also depend on the state of the game; for instance it could...

paper-and-pencil game". DeepFUN. 2015-08-04. Retrieved 2016-12-04. Ferguson, Thomas S. (2014), "Part I: Impartial Combinatorial Games" (PDF), Game Theory (2nd ed...

prizes are given away; as a result, such promotions are handled by an impartial third-party company. McDonald's had a relationship with Simon Worldwide...

one or two coins, the first player will win the game in the next move. Fibonacci nim is an impartial game in that the moves that are available from any...

fuzzy game Dots and boxes Impartial game Digital sum Nim Nimber Sprague–Grundy theorem Partizan game Solved board games Col game Sim (pencil game) Sprouts...

shrinking board and an object that promotes sacrifice combinations. It is impartial: since neither player owns on-board pieces, maintaining the initiative...